Curve detail

Definition

Name secp112r1 (secg/secp112r1, wtls/wap-wsg-idm-ecid-wtls6)
Category secg
Description A randomly generated curve. [SEC2v1](https://www.secg.org/SEC2-Ver-1.0.pdf) states 'E was chosen verifiably at random as specified in ANSI X9.62 [1] from the seed'.
Field Prime (0xdb7c2abf62e35e668076bead208b)
Field bits 112
Form Weierstrass $y^2 = x^3 + ax + b$
Param $a$ 0xdb7c2abf62e35e668076bead2088
Param $b$ 0x659ef8ba043916eede8911702b22
Generator $x$ 0x09487239995a5ee76b55f9c2f098
Generator $y$ 0xa89ce5af8724c0a23e0e0ff77500
Simulation seed 0xf50b028e4d696e676875615175290472783fb1

Characteristics

Order 0xdb7c2abf62e35e7628dfac6561c5
Cofactor 0x1
$j$-invariant 0xadad8cacc8dd210422960337beca
Trace $t$ -0xfa868edb84139
Embedding degree $k$ 0xdb7c2abf62e35e7628dfac6561c4
CM discriminant -0x36cfb7fe7ccf1fcdd86299e26837b

Traits

$\text{discriminant}()$
cm_disc -0x36cfb7fe7ccf1fcdd86299e26837b
factorization ['0x35', '0x108bfd95477d520dd70f469b4aef']
max_conductor 0x1
$\text{twist_order}(deg=1)$
twist_cardinality 0xdb7c2abf62e35e56d80dd0f4df53
factorization None
$\text{twist_order}(deg=2)$
twist_cardinality 0xbc2dad5ce3bc2b4e238afa969c17239d881126f438ddec4b3334c915
factorization None
$\text{kn_factorization}(k=1)$
(+)factorization ['0x2', '0x3', '0x3', '0xc319098dad3be23024550b04c8b']
(+)largest_factor_bitlen 0x6c
(-)factorization ['0x2', '0x2', '0x29', '0x35b', '0x661aedbb7d5022c18e27c86b']
(-)largest_factor_bitlen 0x5f
$\text{kn_factorization}(k=2)$
(+)factorization ['0x1b6f8557ec5c6bcec51bf58cac38b']
(+)largest_factor_bitlen 0x71
(-)factorization ['0x3', '0x5', '0xe1ac9e43', '0x21327c01eb7594f0408d']
(-)largest_factor_bitlen 0x4e
$\text{kn_factorization}(k=3)$
(+)factorization ['0x2', '0x2', '0x2', '0x2', '0x5', '0x5', '0x7', '0xb', '0x23d5', '0x329c383bd', '0xc5c80d71f0951']
(+)largest_factor_bitlen 0x34
(-)factorization ['0x2', '0x3d', '0x65', '0xdae1209d9de8d986bec337737']
(-)largest_factor_bitlen 0x64
$\text{kn_factorization}(k=4)$
(+)factorization ['0x3', '0x10f', '0x7b5', '0x15ef9', '0x1a29d35dc42e3165066d']
(+)largest_factor_bitlen 0x4d
(-)factorization ['0x7', '0xbf', '0x3d7', '0x2bc7454b5e27ebe791b8054d']
(-)largest_factor_bitlen 0x5e
$\text{kn_factorization}(k=5)$
(+)factorization ['0x2', '0x3b03', '0xbacb', '0xcbe50f12060ba33525a8d']
(+)largest_factor_bitlen 0x54
(-)factorization ['0x2', '0x2', '0x2', '0x3', '0xd', '0x1a99d0c6672e7b', '0x21d9b95ed452b7']
(-)largest_factor_bitlen 0x36
$\text{kn_factorization}(k=6)$
(+)factorization ['0x5c9', '0x11fb3', '0xca8e0140ba7107bbc9debd']
(+)largest_factor_bitlen 0x58
(-)factorization ['0x4f', '0xa7', '0xfa97b', '0x1a1ae40a21a23ce2031cf']
(-)largest_factor_bitlen 0x51
$\text{kn_factorization}(k=7)$
(+)factorization ['0x2', '0x2', '0x3', '0x1d', '0x49d', '0x2c9f6ff', '0x7ffa9c5', '0xafb80554121']
(+)largest_factor_bitlen 0x2c
(-)factorization ['0x2', '0x5', '0x11', '0x8b', '0x17b', '0xb3e316477c4288dbafb7985']
(-)largest_factor_bitlen 0x5c
$\text{kn_factorization}(k=8)$
(+)factorization ['0x5', '0xd', '0x3b3', '0x611', '0x13429a2fd89d2f80a383dc3']
(+)largest_factor_bitlen 0x59
(-)factorization ['0x3', '0x3', '0xb', '0x4a881', '0x3ceb84848401affbc764ded']
(-)largest_factor_bitlen 0x5a
$\text{torsion_extension}(l=2)$
least 0x3
full 0x3
relative 0x1
$\text{torsion_extension}(l=3)$
least 0x8
full 0x8
relative 0x1
$\text{torsion_extension}(l=5)$
least 0x8
full 0x8
relative 0x1
$\text{torsion_extension}(l=7)$
least 0x3
full 0x6
relative 0x2
$\text{torsion_extension}(l=11)$
least 0x78
full 0x78
relative 0x1
$\text{torsion_extension}(l=13)$
least 0x18
full 0x18
relative 0x1
$\text{torsion_extension}(l=17)$
least 0x8
full 0x10
relative 0x2
$\text{conductor}(deg=2)$
ratio_sqrt 0xfa868edb84139
factorization ['0x5', '0xd', '0x16f', '0x28d', '0x10dd2c33']
$\text{conductor}(deg=3)$
ratio_sqrt 0xda86ffa9a447e1aa04c5621f21da
factorization ['0x2', '0x1d', '0x1d', '0x71cb', '0x4ad317ad0aa745ac7240ef']
$\text{conductor}(deg=4)$
ratio_sqrt 0x1aca551801c30a182dfa456d09258edc0663ee6d7d
factorization ['0x3', '0x5', '0xd', '0x3d', '0x16f', '0x1e7', '0x28d', '0x111f2cf', '0x10dd2c33', '0xe1843d15', '0x155adf0e73f']
$\text{embedding}()$
embedding_degree_complement 0x1
complement_bit_length 0x1
$\text{class_number}()$
upper 0x2e766b29b64c3406
lower 0x1
$\text{small_prime_order}(l=2)$
order 0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length 0x1
$\text{small_prime_order}(l=3)$
order 0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length 0x1
$\text{small_prime_order}(l=5)$
order 0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length 0x1
$\text{small_prime_order}(l=7)$
order 0x6dbe155fb171af3b146fd632b0e2
complement_bit_length 0x2
$\text{small_prime_order}(l=11)$
order 0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length 0x1
$\text{small_prime_order}(l=13)$
order 0xdb7c2abf62e35e7628dfac6561c4
complement_bit_length 0x1
$\text{division_polynomials}(l=2)$
factorization [['0x3', '0x1']]
len 0x1
$\text{division_polynomials}(l=3)$
factorization [['0x4', '0x1']]
len 0x1
$\text{division_polynomials}(l=5)$
factorization [['0x4', '0x3']]
len 0x1
$\text{volcano}(l=2)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=3)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=5)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=7)$
crater_degree 0x2
depth 0x0
$\text{volcano}(l=11)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=13)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=17)$
crater_degree 0x2
depth 0x0
$\text{volcano}(l=19)$
crater_degree 0x0
depth 0x0
$\text{isogeny_extension}(l=2)$
least 0x3
full 0x3
relative 0x1
$\text{isogeny_extension}(l=3)$
least 0x4
full 0x4
relative 0x1
$\text{isogeny_extension}(l=5)$
least 0x2
full 0x2
relative 0x1
$\text{isogeny_extension}(l=7)$
least 0x1
full 0x6
relative 0x6
$\text{isogeny_extension}(l=11)$
least 0xc
full 0xc
relative 0x1
$\text{isogeny_extension}(l=13)$
least 0x2
full 0x2
relative 0x1
$\text{isogeny_extension}(l=17)$
least 0x1
full 0x10
relative 0x10
$\text{isogeny_extension}(l=19)$
least 0x14
full 0x14
relative 0x1
$\text{trace_factorization}(deg=1)$
trace -0xfa868edb84139
trace_factorization ['0x5', '0xd', '0x16f', '0x28d', '0x10dd2c33']
number_of_factors 0x5
$\text{trace_factorization}(deg=2)$
trace -0xfa868edb84139
trace_factorization ['0x3', '0x3d', '0x1e7', '0x111f2cf', '0xe1843d15', '0x155adf0e73f']
number_of_factors 0x6
$\text{isogeny_neighbors}(l=2)$
len 0x0
$\text{isogeny_neighbors}(l=3)$
len 0x0
$\text{isogeny_neighbors}(l=5)$
len 0x0
$\text{q_torsion}()$
Q_torsion 0x1
$\text{hamming_x}(weight=1)$
x_coord_count 0x3a
expected 0x38
ratio 0.96552
$\text{hamming_x}(weight=2)$
x_coord_count 0xc26
expected 0xc24
ratio 0.99936
$\text{hamming_x}(weight=3)$
x_coord_count 0x1be4c
expected 0x1bd28
ratio 0.99744
$\text{square_4p1}()$
p 0x1
order 0x1
$\text{pow_distance}()$
distance 0x2483d5409d1ca189d720539a9e3b
ratio 6.01082
distance 32 0x5
distance 64 0x5
$\text{multiples_x}(k=1)$
Hx 0x9487239995a5ee76b55f9c2f098
bits 0x6c
difference 0x4
ratio 0.96429
$\text{multiples_x}(k=2)$
Hx 0xaa8728a0279bd6d44e8c99c573e7
bits 0x70
difference 0x0
ratio 1.0
$\text{multiples_x}(k=3)$
Hx 0x71b29d6bd4cc566539bf5644a154
bits 0x6f
difference 0x1
ratio 0.99107
$\text{multiples_x}(k=4)$
Hx 0xd41907b39931dffa6103ffbc8c2c
bits 0x70
difference 0x0
ratio 1.0
$\text{multiples_x}(k=5)$
Hx 0xa29c1051c271f7338c08444f4783
bits 0x70
difference 0x0
ratio 1.0
$\text{multiples_x}(k=6)$
Hx 0xa0f134694e5c834e7c00b9674359
bits 0x70
difference 0x0
ratio 1.0
$\text{multiples_x}(k=7)$
Hx 0x1c715b2f7acf3dd1e2dbc2d296fc
bits 0x6d
difference 0x3
ratio 0.97321
$\text{multiples_x}(k=8)$
Hx 0x8ebafec5962bc4aa17f901910ce
bits 0x6c
difference 0x4
ratio 0.96429
$\text{multiples_x}(k=9)$
Hx 0x268f1146825d33758a143e8c663b
bits 0x6e
difference 0x2
ratio 0.98214
$\text{multiples_x}(k=10)$
Hx 0xd4153672fa25b82d85c3fb51962e
bits 0x70
difference 0x0
ratio 1.0
$\text{x962_invariant}()$
r 0x29e49e36f941c1b2dc1fb82b5bce
$\text{weierstrass}()$
a 0xdb7c2abf62e35e668076bead2088
b 0x659ef8ba043916eede8911702b22